Bistability of platicon solutions in normal dispersion photonic crystal resonators

Frequency comb generation in normal dispersion microresonators has become increasingly more competitive due to advances that take advantage of mode splitting. Examples include the use of injection locking to induce a mode split, coupling of multiple resonators, and the use of photonic crystal resonators (PhCR) in which a grating is inscribed on the inner or outer wall of the resonator. When the split mode is pumped, complex dark pulses often called platicons can form. In this work, we examine the stability of platicons in the pump-power and pump-detuning parameter space in a PhCR with different mode splittings. We show that regions of bistability can occur in which two platicon solutions are stable. We also show that broad regions of stability exist in which the bistability can be avoided.